Proton-Antiproton Annihilation in Baryonium

A possible interpretation of the near-threshold enhancement in the $(p\bar{p})$-mass spectrum in $J\mathrm{/}\psi \to \gamma p\bar{p}$ is the of existence of a narrow baryonium resonance X(1860). Mesonic decays of the $(p\bar{p})$-bound state X(1860) due to the nucleon-antinucleon annihilation are investigated in this paper. Mesonic coherent states with fixed $G$-parity and $P$-parity have been constructed . The Amado-Cannata-Dedoder-Locher-Shao formulation(Phys Rev Lett. {\bf 72}, 970 (1994)) is extended to the decays of the X(1860). By this method, the branch-fraction ratios of $Br(X\to \eta 4\pi)$,$Br(X\to \eta 2\pi)$and$Br(X\to 3\eta)$ are calculated. It is shown that if the X(1860) is a bound state of $(p\bar{p})$, the decay channel ($X\to \eta 4\pi)$isfavoredover$(X\to \eta 2\pi)$. In this way, we develop criteria for distinguishing the baryonium interpretation for the near-threshold enhancement effects in $(p\bar{p})$-mass spectrum in $J/\psi{\to}\gamma p{\bar p}$ from other possibilities. Experimental checks are expected. An intuitive picture for our results is discussed.